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Discrete Mathematics

Fibonacci Numbers

Challenge Quizzes

Fibonacci Numbers: Level 3 Challenges

         

Compute \[ \frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \dots + \frac{F_k}{2^k} + \dots \] where \( F_k\) represents the the \( k^\text{th} \) term of the Fibonacci sequence: \(1, 1, 2, 3, 5, 8, 13, ... \)

Find the last digit of the 123456789-th Fibonacci number.

In the Fibonacci sequence, \(F_{0}=1\), \({F_1}=1\), and for all \(N>1\), \(F_N=F_{N-1}+F_{N-2}\).

How many of the first 2014 Fibonacci terms end in 0?

The Fibonacci sequence is defined by \(F_1 = 1, F_2 = 1\) and \( F_{n+2} = F_{n+1} + F_{n}\) for \( n \geq 1 \).

Find the greatest common divisor of \(F_{484}\) and \(F_{2013}\).

\[\sum_{n=0}^{\infty} \frac{F_{n}}{3^{n}}= \ ? \]

Details and Assumptions

\(F_{n}\) is the \(n^\text{th} \) Fibonacci number, with \(F_{1} = F_{2} = 1\).

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